Lesson 3.3: Measurement – Area of Compound Shapes & Combined Area/Perimeter Word Problems | SEA Mathematics | My Carib Academy
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📏 Lesson 3.3: Measurement – Area of Compound Shapes & Combined Area/Perimeter

Master area of compound shapes and combined area & perimeter word problems. This lesson covers SEA Mathematics Objectives 152-155 from the Measurement Strand.

65 Minutes
Module 3: Measurement
Objectives 152-155
2 Videos
Lesson Progress 0%

Previous Lesson

Did you complete Lesson 3.2? Review Perimeter & Area →

Learning Objectives

By the end of this lesson, you will be able to:

  • Calculate area of compound shapes by splitting into rectangles (Objective 152)
  • Solve word problems involving both area and perimeter (Objectives 153-154)
  • Determine when to use area vs perimeter in real-life situations (Objective 155)
  • Solve multi-step measurement problems

SEA Tip

Area and perimeter word problems appear in Section II and III of the SEA Math paper. These are worth 2-4 marks each! (SEA Framework Page 25-26)

Watch: Perimeter Word Problems

Start by watching this video to learn how to solve perimeter word problems. Take notes as you watch! 📝

Perimeter Word Problems – Mathematics Video Lesson

Quick Check

Did you understand the video? Review the notes below before continuing! ✅

Area of Compound Shapes

Compound shapes are made by combining two or more simple shapes. To find the area, split the shape into rectangles!

How to Find Area of Compound Shapes

  1. Split the compound shape into rectangles
  2. Find any missing side lengths
  3. Calculate the area of each rectangle (A = l × w)
  4. Add all the areas together
  5. Include square units (cm², m²)

📊 Example 1: L-Shaped Compound Shape

6 cm 3 cm 5 cm 3 cm A = 18 cm² A = 15 cm²

L-Shape

Rectangle 1: 6 × 3 = 18 cm²
Rectangle 2: 3 × 5 = 15 cm²
Total Area = 33 cm²

📊 Example 2: T-Shaped Compound Shape

Finding Area Step-by-Step

Question: Find the area of this T-shaped compound shape.

Solution:

  1. Split into 2 rectangles: Top rectangle and bottom rectangle
  2. Top rectangle: 10 cm × 4 cm = 40 cm²
  3. Bottom rectangle: 4 cm × 6 cm = 24 cm²
  4. Total area: 40 + 24 = 64 cm²

Answer: 64 cm²

Common Mistake

Don’t forget to find missing sides before calculating! Use the given measurements to work out unknown lengths.

Watch: Combined Area & Perimeter Word Problems

Now watch this video to learn how to solve word problems involving both area and perimeter. Pay attention! 🎯

Area and Perimeter Word Problems – Mathematics Video Lesson

Combined Area & Perimeter Word Problems

Sometimes you need to use BOTH area and perimeter to solve real-life problems!

📋 When to Use Area vs Perimeter:

Key Words to Look For
Use PERIMETER When: Use AREA When:
Fencing around a garden Grass inside a garden
Frame around a picture Paint on a wall
Border around a room Carpet for a floor
Walking around a field Tiles for a floor

📊 Example 3: Combined Word Problem

Fencing and Grass for a Garden

Question: A rectangular garden is 12 m long and 8 m wide. Find: (a) The length of fencing needed (b) The area of grass needed

Solution:

  1. (a) Perimeter (fencing): P = 2 × (12 + 8) = 2 × 20 = 40 m
  2. (b) Area (grass): A = 12 × 8 = 96 m²

Answer: (a) 40 m of fencing, (b) 96 m² of grass

📊 Example 4: Multi-Step Word Problem

Painting a Wall with a Window

Question: A wall is 5 m long and 3 m high. There is a window that is 2 m by 1 m. Find the area of wall to be painted (excluding the window).

Solution:

  1. Area of wall: 5 × 3 = 15 m²
  2. Area of window: 2 × 1 = 2 m²
  3. Area to paint: 15 − 2 = 13 m²

Answer: 13 m² to be painted

Memory Trick

Perimeter = AROUND the outside (fence, border, frame)
Area = INSIDE the space (grass, paint, carpet, tiles)
Compound Shapes = SPLIT into rectangles, then ADD areas

Quick Quiz

Test your understanding! Select an answer for each question. 📏

6 Questions
12 Minutes
70% to Pass

1. An L-shape is split into two rectangles: 6 cm × 4 cm and 3 cm × 5 cm. What is the total area?

2. A rectangle is 10 m long and 6 m wide. What is the perimeter?

3. A rectangle is 10 m long and 6 m wide. What is the area?

4. A wall is 20 m². A window is 4 m². What area needs painting?

5. What do you need to find for fencing around a garden?

6. What do you need to find for carpet for a floor?

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Lesson Complete!

Great job finishing Lesson 3.3! You’re mastering area and perimeter for the SEA exam! 🎉

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